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Theorem rexrab2 3004
Description: Existential quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)
Hypothesis
Ref Expression
ralab2.1
Assertion
Ref Expression
rexrab2
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem rexrab2
StepHypRef Expression
1 df-rab 2623 . . 3
21rexeqi 2812 . 2
3 ralab2.1 . . 3
43rexab2 3003 . 2
5 anass 630 . . . 4
65exbii 1582 . . 3
7 df-rex 2620 . . 3
86, 7bitr4i 243 . 2
92, 4, 83bitri 262 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wcel 1710  cab 2339  wrex 2615  crab 2618
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-rab 2623
This theorem is referenced by: (None)
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